Approximate Coloring of Uniform Hypergraphs (Extended Abstract) [chapter]

Michael Krivelevich, Benny Sudakov
<span title="">1998</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We consider an algorithmic problem of coloring r-uniform hypergraphs. The problem of nding the exact value of the chromatic number of a hypergraph is known to be NP-hard, so we discuss approximate solutions to it. Using a simple construction and known results on hardness of graph coloring, we show that for any r 3 it is impossible to approximate in polynomial time the chromatic number of r-uniform hypergraphs on n vertices within a factor n 1? for any > 0, unless NP ZPP. On the positive side,
more &raquo; ... present an approximation algorithm for coloring r-uniform hypergraphs on n vertices, whose performance ratio is O(n(log log n) 2 =(log n) 2 ). We also describe an algorithm for coloring 3-uniform 2-colorable hypergraphs on n vertices inÕ(n 9=41 ) colors, thus improving previous results of Chen and Frieze and of Kelsen, Mahajan and Ramesh.
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